Predictive Performance of Deep Quantum Data Re-uploading Models

TL;DR

This paper investigates the limitations of deep quantum data re-uploading models, revealing that increasing encoding layers can cause predictive performance to deteriorate to near random guessing, especially with high-dimensional data.

Contribution

It provides a theoretical analysis showing the degradation of predictive performance in deep data re-uploading models and offers practical design guidance for quantum circuits.

Findings

Performance degrades with more encoding layers in high-dimensional data.

Deeper models do not necessarily improve predictions, often leading to near-random results.

Wider circuit architectures are recommended over deeper ones for better performance.

Abstract

Quantum machine learning models incorporating data re-uploading circuits have garnered significant attention due to their exceptional expressivity and trainability. However, their ability to generate accurate predictions on unseen data, referred to as the predictive performance, remains insufficiently investigated. This study reveals a fundamental limitation in predictive performance when deep encoding layers are employed within the data re-uploading model. Concretely, we theoretically demonstrate that when processing high-dimensional data with limited-qubit data re-uploading models, their predictive performance progressively degenerates to near random-guessing levels as the number of encoding layers increases. In this context, the repeated data uploading cannot mitigate the performance degradation. These findings are validated through experiments on both synthetic linearly separable datasets and real-world datasets. Our results demonstrate that when processing high-dimensional data, the quantum data re-uploading models should be designed with wider circuit architectures rather than deeper and narrower ones.